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Java > Open Source Codes > org > apache > commons > math > analysis > SecantSolver


1 /*
2  * Copyright 2003-2004 The Apache Software Foundation.
3  *
4  * Licensed under the Apache License, Version 2.0 (the "License");
5  * you may not use this file except in compliance with the License.
6  * You may obtain a copy of the License at
7  *
8  * http://www.apache.org/licenses/LICENSE-2.0
9  *
10  * Unless required by applicable law or agreed to in writing, software
11  * distributed under the License is distributed on an "AS IS" BASIS,
12  * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
13  * See the License for the specific language governing permissions and
14  * limitations under the License.
15  */
16 package org.apache.commons.math.analysis;
17
18 import java.io.Serializable JavaDoc;
19
20 import org.apache.commons.math.ConvergenceException;
21 import org.apache.commons.math.FunctionEvaluationException;
22
23
24 /**
25  * Implements a modified version of the
26  * <a HREF="http://mathworld.wolfram.com/SecantMethod.html">secant method</a>
27  * for approximating a zero of a real univariate function.
28  * <p>
29  * The algorithm is modified to maintain bracketing of a root by successive
30  * approximations. Because of forced bracketing, convergence may be slower than
31  * the unrestricted secant algorithm. However, this implementation should in
32  * general outperform the
33  * <a HREF="http://mathworld.wolfram.com/MethodofFalsePosition.html">
34  * regula falsi method.</a>
35  * <p>
36  * The function is assumed to be continuous but not necessarily smooth.
37  *
38  * @version $Revision$ $Date: 2005-06-03 22:36:42 -0700 (Fri, 03 Jun 2005) $
39  */
40 public class SecantSolver extends UnivariateRealSolverImpl implements Serializable JavaDoc {
41     
42     /** Serializable version identifier */
43     static final long serialVersionUID = 1984971194738974867L;
44     
45     /**
46      * Construct a solver for the given function.
47      * @param f function to solve.
48      */
49     public SecantSolver(UnivariateRealFunction f) {
50         super(f, 100, 1E-6);
51     }
52
53     /**
54      * Find a zero in the given interval.
55      *
56      * @param min the lower bound for the interval
57      * @param max the upper bound for the interval
58      * @param initial the start value to use (ignored)
59      * @return the value where the function is zero
60      * @throws ConvergenceException if the maximum iteration count is exceeded
61      * @throws FunctionEvaluationException if an error occurs evaluating the
62      * function
63      * @throws IllegalArgumentException if min is not less than max or the
64      * signs of the values of the function at the endpoints are not opposites
65      */
66     public double solve(double min, double max, double initial)
67         throws ConvergenceException, FunctionEvaluationException {
68             
69         return solve(min, max);
70     }
71     
72     /**
73      * Find a zero in the given interval.
74      * @param min the lower bound for the interval.
75      * @param max the upper bound for the interval.
76      * @return the value where the function is zero
77      * @throws ConvergenceException if the maximum iteration count is exceeded
78      * @throws FunctionEvaluationException if an error occurs evaluating the
79      * function
80      * @throws IllegalArgumentException if min is not less than max or the
81      * signs of the values of the function at the endpoints are not opposites
82      */
83     public double solve(double min, double max) throws ConvergenceException,
84         FunctionEvaluationException {
85         
86         clearResult();
87         verifyInterval(min, max);
88         
89         // Index 0 is the old approximation for the root.
90 // Index 1 is the last calculated approximation for the root.
91 // Index 2 is a bracket for the root with respect to x0.
92 // OldDelta is the length of the bracketing interval of the last
93 // iteration.
94 double x0 = min;
95         double x1 = max;
96         double y0 = f.value(x0);
97         double y1 = f.value(x1);
98         
99         // Verify bracketing
100 if (y0 * y1 >= 0) {
101             throw new IllegalArgumentException JavaDoc
102             ("Function values at endpoints do not have different signs." +
103                     " Endpoints: [" + min + "," + max + "]" +
104                     " Values: [" + y0 + "," + y1 + "]");
105         }
106         
107         double x2 = x0;
108         double y2 = y0;
109         double oldDelta = x2 - x1;
110         int i = 0;
111         while (i < maximalIterationCount) {
112             if (Math.abs(y2) < Math.abs(y1)) {
113                 x0 = x1;
114                 x1 = x2;
115                 x2 = x0;
116                 y0 = y1;
117                 y1 = y2;
118                 y2 = y0;
119             }
120             if (Math.abs(y1) <= functionValueAccuracy) {
121                 setResult(x1, i);
122                 return result;
123             }
124             if (Math.abs(oldDelta) <
125                 Math.max(relativeAccuracy * Math.abs(x1), absoluteAccuracy)) {
126                 setResult(x1, i);
127                 return result;
128             }
129             double delta;
130             if (Math.abs(y1) > Math.abs(y0)) {
131                 // Function value increased in last iteration. Force bisection.
132 delta = 0.5 * oldDelta;
133             } else {
134                 delta = (x0 - x1) / (1 - y0 / y1);
135                 if (delta / oldDelta > 1) {
136                     // New approximation falls outside bracket.
137 // Fall back to bisection.
138 delta = 0.5 * oldDelta;
139                 }
140             }
141             x0 = x1;
142             y0 = y1;
143             x1 = x1 + delta;
144             y1 = f.value(x1);
145             if ((y1 > 0) == (y2 > 0)) {
146                 // New bracket is (x0,x1).
147 x2 = x0;
148                 y2 = y0;
149             }
150             oldDelta = x2 - x1;
151             i++;
152         }
153         throw new ConvergenceException("Maximal iteration number exceeded" + i);
154     }
155
156 }
157
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